Do You Know Affine Braid Group?

10 Questions | By Gregorynaomi | Last updated: Mar 19, 2022 | Total Attempts: 105

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What is your knowledge on Affine Braid Group? You can find out by taking this quiz. On a brief note, An Affine Braid Group is a braid group associated to an affine Coxeter system. Their group rings have quotients called affine Hecke algebras. They are subgroups of double affine braid groups. How well do you know about this? Choose the correct answers to the accompany questions to find out.

Questions and Answers

1.

The generalization to other values of n will be straightforward in an affine braid group, if?
- A.
  
  N=4
- B.
  
  N=2
- C.
  
  N=0
- D.
  
  N=-2
2.

In an affine braid group the set of all braids on four strands is denoted by?
- A.
  
  B4
- B.
  
  B3
- C.
  
  B2
- D.
  
  B7
3.

One major property of affine braid group is that all non-identity elements of Bn posses?
- A.
  
  Infinite order
- B.
  
  Linear order
- C.
  
  Finite order
- D.
  
  Parallel order
4.

The left-invariant linear order on Bn in a braid group is known as?
- A.
  
  Infinite order
- B.
  
  Dehomoy order
- C.
  
  Parallel order
- D.
  
  Finite prism
5.

One thing to note when relating symmetric group with affine braid group is that?
- A.
  
  Every braid on n strands are different on n elements
- B.
  
  Every braid on n strands determines a permutation on p elements
- C.
  
  Every braid on n strands is linear to n elements
- D.
  
  Every braid on n strands determines a permutation on n elements
6.

Which of the following braid group is the universal central extension of the modular group PSL(2, Z)?
- A.
  
  B1
- B.
  
  B2
- C.
  
  B3
- D.
  
  B4
7.

The affine group that posses group rings with quotients called double affine Hecke algebras is called.
- A.
  
  Double affine group
- B.
  
  Hecke affine group
- C.
  
  Ring based affine group
- D.
  
  Weyl affine group
8.

An affine braid group is a braid group generally associated with which mathematical system?
- A.
  
  Affine ring system
- B.
  
  Affine Coxeter system
- C.
  
  Affine Coter system
- D.
  
  Affine double system
9.

One way to represent concretely the Elements of the braid group is via?
- A.
  
  Decimals
- B.
  
  Indices
- C.
  
  Matrices
- D.
  
  Coefficients
10.

The Lawrence representations depending on several parameters for affine brai group was postulated in what year?
- A.
  
  1990
- B.
  
  1992
- C.
  
  1991
- D.
  
  1993